Measuring Galaxy Potentials using Shell Kinematics

We show that the kinematics of the shells seen around some elliptical galaxies provide a new, independent means for measuring the gravitational potentials of elliptical galaxies out to large radii. A numerical simulation of a set of shells formed in the merger between an elliptical and a smaller galaxy reveals that the shells have a characteristic observable kinematic structure, with the maximum line-of-sight velocity increasing linearly as one moves inward from a shell edge. A simple analytic calculation shows that this structure provides a direct measure of the gradient of the gravitational potential at the shell radius. In order to extract this information from attainable data, we have also derived the complete distribution of line-of-sight velocities for material within a shell; comparing the observed spectra of a shell to a stellar template convolved with this distribution will enable us to measure the gradient of the potential at this radius. Repeating the analysis for a whole series of nested shells in a galaxy allows the complete form of the gravitational potential as a function of radius to be mapped out. The requisite observations lie within reach of the up-coming generation of large telescopes.